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48 = (a) Experiment (Hjorth,1975) =3 5 7 3 9 11 1 Flow -1 -0.5 0 0.5 X/B (b) Numerical Figure 6.2. Comparison of bed shear stress distribution (N/m2) around a circular pier as calculated from an experiment by Hjorth (1975) and numerical computations (B = 0.075 m, V = 0.30 m/s, H = 0.2 m). By regression, the equation proposed for the correction 6.7 PIER SPACING EFFECT: factor kw giving the influence of the water depth on the max- NUMERICAL SIMULATION RESULTS imum shear stress is The objective of this parametric study is to obtain the rela- max - 4H tionship between the maximum bed shear stress max and pier kw = = 1 + 16e B (6.2) max (deep) spacing (Figure 6.11). One of the flume experiments was chosen to perform the numerical simulation. The cylindrical pier had a diameter of 0.16 m and was placed vertically in a 1.5-m-wide flume. The mean depth approach velocity was 0.33 m/s and the water depth is 0.375 m. Four different pier spacings were simu- H lated: S/ B = 6 (in the case of one pile in the flume), S/ B = Flow 3.12 (in the case of two piles), S/ B = 2.34 (in the case of three piles), and S/ B = 1.88 (in the case of four piles). The Reynolds Number based on diameter was Re = 52800 and the Froude Number based on diameter was Fr = 0.2634. The B velocity between the piles became higher due to the de- Figure 6.3. Problem definition for water depth effect. creased spacing and the corresponding shear stress increases.